The concept is very simple: if the information is unnecessary either to the sentence structure or to the meaning of the sentence, then wrap it in commas. However, of all the rules this is the one that I find myself double guessing my first instincts on because sometimes the commas are optional and sometimes they are not.
What Does Parenthetical Mean?
Parenthetical literally just means enclosed in parenthesis, but in the case of this rule, it means that it could be in parenthesis.
This sort of non-essential information adds interesting information, but the information is not always necessary either to the clarity of the meaning or to the sentence structure.
Common Types of Parenthetical Information:
Parenthetical information can do all sorts of things for your sentences. Here are a few of the most common types.
Introductory Clauses
Introductory clauses contain information at the start of the sentence that gives context to the main idea.
Example: In Romeo and Juliet, the Nurse acts as a surrogate mother in more ways than one.
Exceptions: in short and simple sentences where the introductory information is only a few words, the comma can be optional. However, when the sentence is more complex and the introductory clause is longer, the comma is necessary for clarity.
Further Details
Further details are just additional details that do not change the meaning of the sentence or provide necessary information anywhere within the sentence.
Example: William Shakespeare's wife, Ann Hathaway, was likewise of an ignoble birth and no doubt would be forgotten to history if not for her husband.
Exception: If the information is necessary for understanding the sentence, then it does not go in commas. If we were talking about Henry VI's wife, we would need to specify which one by name because he had several, so her name would not be in commas. Since Shakespeare only had one wife, her name is less necessary for understanding whom we are talking about.
Asides
Asides are commentary from the author, often containing wit or humor. Example: One of Shakespeare's most well known histories, though perhaps least worthy of being called historical, is Henry V.
Exception: If the aside is particularly long or the sentence already has several clauses with commas, parenthesis or dashes may be more appropriate punctuation for ease of reading.
A Word About Style
Of all the comma rules, this one is the most subjective and malleable. Different style guides and editors may have different opinions about when information counts as parenthetical. As always, if you want some help figuring out your style or following a style manual, just let me know. The contact button is right there.